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Friday, October 14, 2011

AdS/CFT confronts data

One of the most persistent and contagious side-effects of string theory has been the conjectured AdS/CFT correspondence (that we previously discussed here, here and here). The briefest of all brief summaries is that it is a duality that allows to swap the strong coupling limit of a conformal field theory (CFT) with (super)gravity in a higher dimensional Anti-de-Sitter (AdS) space. Since computation at strong coupling is difficult, at the very least this is a useful computational tool. It has been applied to some condensed matter systems and also to heavy ion physics, where one wants to know the properties of the quark gluon plama. Now the theory that one has to deal with in heavy ion collisions is QCD, which is neither supersymmetric nor conformal, but there have been some arguments for why it should be approximately okay.

The great thing about the application of AdS/CFT to heavy ion physics is that it made predictions for the LHC's heavy ion runs that are now being tested. One piece of data that is presently coming in is the distribution of jets in heavy ion collisions, but first some terminology.

A heavy ion is an atom with a high atomic number stripped of all electrons; typically one uses lead or gold. Compared to a proton, a heavy ion is a large clump of bound nucleons (neutrons and protons) that are accelerated and brought to collision. They may collide head-on or only peripherally, quantified in a number called "centrality." When the ions collide, they temporarily form a hot, dense soup of quarks and gluons called the "quark gluon plasma." This plasma rapidly expands and cools and the quarks and gluons form hadrons again (in a process called "hadronization" or also "fragmentation"), that are then detected. The temperature of the plasma depends on the energy of the colliding ions that is provided by the accelerator. At RHIC the temperature is about 350 MeV, in the LHC's heavy ion program it is about 500 MeV. The task of heavy ion physicists is to extract information about matter at nuclear densities and such high temperatures from the detected collision products.

A (di) jet is two back-to-back correlated showers of particles that are a typical signature in perturbative QCD. It is created if a pair of outgoing partons (quarks or gluons) hadronizes and produces a bunch of particles that then hit the detector. Since QCD is confined, the primary, colored, particles never reach the detector. In contrast to proton-proton collisions, in heavy ion collisions the partons have to first go through the quark gluon plasma before they can make a jet. Thus, the distribution of momenta of the observed jets depends on the properties of the plasma, in particular the energy loss that the partons undergo.

Different models predict different energy loss and dependence of that energy loss on the temperature of the medium. Jets are a QCD feature at weak coupling and strictly speaking in the strong coupling limit that AdS/CFT describes there are no jets at all. What one can however do is to use a hybrid model in which one just extracts the energy loss in the plasma from the conformal theory. This energy loss scales with L3 T4, where L is the length that the partons travel through the medium and T is the temperature. All other models for the energy loss scale with smaller powers of the temperature.

Heavy ion physicists like to encode observables into how different they are from the corresponding observables for collisions of the ion's constituents. The "nuclear suppression factor," denoted RAA, plotted in Thorsten Renk's figure below (Slide 17 of this talk), is basically the ratio of the cross-section for jets in lead-lead over the same quantity for proton-proton (normalized to the number of nucleons) and it's depicted as a function of the average transverse momentum (pT) of the jets. The black dots are the ALICE data, the solid lines are fits from various models. The orange line at the bottom is AdS/CFT.

As the saying goes, a picture speaks a thousand words, but since links and image sources have a tendency to deteriorate over time, let me spell it out for you: The AdS/CFT scaling does not agree with the data at all.

A readjustment of parameters might move the total curve up or down, but the slope would still be off. Another problem with the AdS/CFT model is that the model parameters needed to fit the RHIC data are very different from the ones needed for the LHC. The model that does best is Yet another Jet Energy-loss Model (YaJEM) that works with in medium showers (I know nothing about that code). It is described in some detail in this paper. It doesn't only fit well with the observed scaling, it also does not require a large readjustment of parameters from RHIC to LHC.

Of course there's always caveats to a conclusion. One might criticize for example the way that AdS/CFT has been implemented into the code. But the scaling with temperature is such a general property that I don't think nagging at the details will be of much use here. Then one may want to point out that the duality is good actually only in the large N limit and N=3 isn't so large after all. And that is right, so maybe one would have to take correction terms more seriously. But that would then require calculating string contributions and one loses the computational advantage that AdS/CFT seemed to bring.

Some more details on the above figure are in Thorsten Renk's proceedings from the Quark Matter 2011, on the arxiv under 1106.2392 [hep-ph].

Summary: I predict applications of the AdS/CFT duality to heavy ion physics is a rapidly cooling area.

A central mystery in quantum condensed matter physics is the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. Field theoretical statistical techniques are useless because of the fermion sign problem, but we will present here results showing that the mathematics of string theory is capable of describing fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theory. Deforming away from the relativistic quantum critical point by increasing the fermion density we show that a state emerges with all the features of the Fermi-liquid. Tuning the scaling dimensions of the critical fermion fields we find that the quasiparticle disappears at a quantum phase transition of a purely statistical nature, not involving any symmetry change. These results are obtained by computing the solutions of a classical Dirac equation in an AdS space time containing a Reissner-Nordstrom black hole, where the information regarding Fermi-Dirac statistics in the field theory is processed by quasi-normal Dirac modes at the outer horizon.

In this respect, I am speaking to the nature of "the viscosity," in both conditions/ particle collisions and Superconductor Tc....I know I will have to be corrected as a faint memory is poking me....yet cannot see it clearly.

Just a few quotes...I can remove them if you feel they are not directly connected to your posting.

"We want to measure when the quark-gluon plasma behaves like a perfect fluid with zero viscosity, and when it doesn't," says Lauret. "When it doesn't match our calculations, what parameters do we have to change? If we can put everything together, we might have a model that reproduces everything we see in our detector." See:Probing the Perfect Liquid with the STAR Grid

They understood what they had to do in terms of probing the characteristics of the collision process.

Using the anti–de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid. See:String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid

The jets too(?)....these are distinctive signatures...and the pic here you will recognize as being deposited amongst our blog comments.

I would imagine Robert would be happy if he could pictorially see the similarity of events in the cosmos "as orbital image correlative" also seen as a "Jet?" ;)

I tend to see the geometrical inclination of such collapses as a part of the "whole picture seen when probing the QGP through collision process." If it's wrong then of course such speculation would have to be seen as a layman who needs definitive education upgrades:)

For those curious, what they mean by "a strong-coupling phenomenological model based on AdS/CFT ideas" is set out in arXiv:0908.0880. It's actually a hybrid model which uses N = 4 super-Yang-Mills for one step, treating the gluon-medium interaction.

AdS/CFT is empirically wrong, as further demonstrated here. How much empirical falsification does physical theory require before it admits to being falsified?

"But AdS/CFT is all we have!" There is no observation that contradicts the vacuum having an intrinsic trace chiral pseudoscalar background toward (fermionic) mass, but not toward photons. Hierarchies of manually inserted symmetry breakings are diagnostic of a defective founding postulate: vacuum isotropy toward mass. Somebody should look. The worst it can do is succeed.

I'm not an expert on energy loss, but I think this is premature. First of all, applying AdS/CFT to energy loss is more difficult then applying it to fluid dynamics, because there is more than one scale.

1) In hydro there is only T, and if \alpha_s(T) is large then it makes sense to use AdS/CFT. Indeed, values of \eta/s extracted at LHC are getting closer and closer to 1/4\pi.

2) For jets there are at least two parameters, a hard scale Q related to the jet, and a soft scale T related to the medium. This means that there is more than one strategy for applying AdS/CFT. i) Ambitious: Everything is strongly coupled; ii) Modest: Only the medium is strongly coupled.

The ambitious strategy must clearly fail for very high p_t jets, and this is what the plot appears to show. (I believe there is some support for the L^3 behavior of the ambitious result at RHIC, and in other LHC data).

In addition to that, there are still some uncertainties in the weak coupling calculations. I find it amusing that the AdS/CFT curve is essentially indistinguishable from ASW, which is a pQCD calculation.

YaJEM is based on the Lund model, which describes hadrons as strings. So this may indeed be a sign that for these processes, one needs to go beyond supergravity to the full AdS superstring, in order to describe them using AdS/CFT.

"The shower code YaJEM is known to have in principle an L^2 dependence due to coherence, but which effectively reduces to L by finite-energy corrections, whereas YaJEM-D has a complicated non-linear pathlength dependence.

So, yeah, I think 'complicated nonlinear' is virtually the same as 'no such simple law.' Best,

Yes, you are right. It is premature to bury AdS/CFT in heavy ion physics as there are different variants in the implementation. But it clearly doesn't look good, even the L^2 scaling is too much. In the end the term 'strongly coupled' should have some relevance. And, yes, I think the RHIC data alone did indicate that a strongly coupled qgp does actually work quite well with the data. (See also summary slid of talk.) Best,

Yet another nice synopsis of the current research to have us to know that the LHC is not all about looking for the elusive Higgs or creating fearsome black holes. In such respect it seems it’s having nature speaking again only more so as to what things can’t be rather than what they can. I must say I didn’t have a clue as to what this YaJEM model might be until Mitchell mentioned it was related to the Lund Model which I gather is not a string theory Per se, yet rather an extension of field theory where gluons are described as self interacting strong color field lines. So from my admittedly novice perspective this seems to simply reinforce field theory rather than give reason why it need be superseded or how.

I am not particularly a believer that QCD can be described by a semiclassical gravity theory, but this confrontation is very VERY far from final:

First of all, no one really knows how to calculate jet energy loss in AdS/CFT. The most general solution (only for quark jets, not for gluon ones) would be the numerical one shown in Fig. 1 of http://arxiv.org/abs/0810.1985You will notice that "rate of energy loss" is ill-defined, as the stopping distance varies _strongly_ with the "initial condition", which basically corresponds to the virtuality of the quark.WHat is the initial parton virtuality in this medium? Well, no one really knows, but a back-of-the-envelope calculation shows that L^3 dependence (infinite energy wrt temperature AND infinite medium length) can not be right (see alsohttp://arxiv.org/abs/1106.1680 ).

Secondly, ruling out a model based on 4 Supersymmetries for heavy ion collisions is, as they say in Italy, like shooting on the red cross. The real question is whether a semiclassical holographic model of any kind provides an acceptable description. Including those where the CFT is broken (either "top-down" or "bottom-up").I do not really believe in these, but they well have the potential of adjusting the increase of Raa with pT you mention.

Bottom line, comparing with data is all well and good but the _theory_ lines on this graph have huge error bars.

More in general, ALL these models, (pQCD AND AdS/CFT)when you look at them in detail, have quite a few more-or-less-hidden parameters you can tweak.None, so far, fit harmonic coefficients of jets. And none fit heavy quarks and light quarks at the same time.

Hi Bee, I'm sorry if that appeared to be out of nowhere -- as a long time reader and netizen I'm fairly certain of the difference between your blog and a more general forum. I hadn't seen eV used as a measure of temperature before (as was done in your post). I did consult Google before asking the question here, making sure I was looking for how it's used in particle physics, but nothing turned up.

Thanks for the link. It appears that it only provides a calculator. I'll start tabulating the values now and see if I can come up with a function to convert one from the other in a few years' time. ;-)